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Weak Dependence Beyond Mixing for Infinite ARCH-type Bilinear Models

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  • Paul Doukhan

    (Crest)

  • Hélène Madre

    (Crest)

  • Mathieu Rosenbaum

    (Crest)

Abstract

Weak dependence properties of ARCH-type bilinear models as introduced by Doukhanand Louhichi (1999) is investigated here. Those models are usually considered for their longrange dependence properties, see Giraitis and Surgailis (2002). Decay of the weak dependencecoefficient sequence are established under different specifications of the model's coefficients.This implies various limit theorems and asymptotics for statistical procedures.We also derivejoint densities for such models in case of regular inputs.

Suggested Citation

  • Paul Doukhan & Hélène Madre & Mathieu Rosenbaum, 2005. "Weak Dependence Beyond Mixing for Infinite ARCH-type Bilinear Models," Working Papers 2005-50, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-50
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    References listed on IDEAS

    as
    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Giraitis, Liudas & Surgailis, Donatas, 0. "ARCH-type bilinear models with double long memory," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 275-300, July.
    3. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    4. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    5. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    6. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    7. Kazakevičius, Vytautas & Leipus, Remigijus, 2002. "On Stationarity In The Arch(∞) Model," Econometric Theory, Cambridge University Press, vol. 18(1), pages 1-16, February.
    8. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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